1) Evaluate the double integral ∬Dx^2 y dA, where D is the top half of the...

1) Evaluate the double integral ∬Dx^2 y dA, where D is the top half of the disc with center the origin and radius 2 by changing to polar coordinates.

2) Use a double integral to find the area of one loop of the rose r= 6cos (3θ).

3) Use polar coordinates to find the volume of the solid below the paraboloid z=50−2x^2−2y^2 and above the xy-plane.

Solutions

Expert Solution

For the given region D, we have, In polar coordinates, x=2 cos and y= 2 sin

Where varies from 0 to and r varies from 0 to 2. The step by step explanatory solution is provided below.

milcah answered 1 year ago

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